See the insightful (and amusing) AN73 from Linear tech (available at
http://www.linear.com/pc/downloadDocument.do?navId=H0,C1,C1003,C1142,C1114,P1134,D4162)
A resistor is
As to the original questions, I started on my own as well and had the
same issues - my first formal education in electronics being provided
at the Air Engineering school, Royal Navy. By then I had successfully
built many a hobby project, but it was quite an epiphany to see the
details of those parts I had used revealed properly. I would note,
however, that the explanation was by way not merely of the books issued
to us, but also the instructors taking the time to explain things in a
synonymous but functional way.
I have used many textbooks when teaching in the U.S. and I have yet to
find one designed for that purpose that truly explained components and
their properties in a non-technical way; yet a student is non-technical
until trained. That's why we had to do our own lesson guides (I still
have all of mine from a decade of teaching) to explain what the
textbook was actually speaking of.
That notwithstanding, there are some great guides that do explain
things in an intuitive way, although the best way is usually to talk to
someone who understands the component.
So - what is a resistor? It's a device that limits current (from one
perspective) or it is used to get a specific voltage across it's
terminals (from another perspective). It is both of these (and more).
The key is to understand what you are trying to achieve with the
component - and there ohm's law (or more properly the algebraic
statement that is a result of ohm's law as G.S.Ohm makes no mention of
the word resistance) is the device that makes it clear. Ignore the
units - rearrange the equaation and see what the result can be.
If you use some method of forcing a current somewhere and there is a
voltage across some device in that current path, it could easily be
called an equivalent resistor (and often is), even though there may be
no resistor in sight (at that part of the circuit, anyway).
Certainly I understand the desire to see a component described without
mathematics, and that is certainly useful. One should remember that
mathematics is a language - so describing things mathematically is
merely using a different language for the description, albeit a
language that can be somewhat arcane and non-intuitive
Cheers
PeteS